Yes, it could be some kind of frequency modulation.
Still, on the oscilloscope's screen, the edges are jumping around a middle position. The jumping seems pretty random to me, it doesn't look like a continuous drift or a modulation, but I didn't made any statistics, so I might be wrong. Next time I will try to record the screen, and post it here. My experience with stable oscillators is zero, it might be just normal to see an edge randomly jumping inside a 100ns range window when looking at 1 second later after the trigger point, I don't know.
I also suspect that the oscilloscope might not use a circular buffer for storing the ADC's samples (which would be crazy, but who knows), and for delays longer than 24ms (max scope's memory is 24 million samples, at a sample rate of 1Gs/s that would be 24ms) the scope is just waiting for the required delay without sampling, then start sampling and memorizing. If this is true, and the waiting delay is calculated using the reference oscillator (25MHz) and not the PLL (1GHz), that might make the seen "jitter" to accumulate for longer delays.
For my own curiosity, for the next step I want to save all 24 Msamples in the PC (for many times) and do some Fourier analysis. The hope here is to clarify if what is seen on the screen is because of a jitter, a drift, a frequency modulation or maybe something else.
For the next measurements, I will try to use the sync output from the generator, as Teneyes PM'ed me, in the hope that the edges from the sync output will be faster then the edges of the signal output, and this will reduce the oscilloscope's trigger jitter. Trigger jitter should not accumulate with the viewing delay, but the more stable, the better.
Also, I searched about jitter accumulation in PLLs, and found a few PDFs online, but didn't have the time to parse them, so I'm not sure yet if the jitter accumulation described in those PDFs is applicable here.
TL;DR
Just to be clear: The 5us PLL jitter bug from a couple of years ago was fixed long time ago. That bug is not present any more in my DS1054Z.
What I am testing here is just because I want to have a better understanding about PLLs in general.